Is it permissible to perform Hajj on behalf of a person who had performed it before he died?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

Scholars have different opinions on whether gifting the reward for a righteous deed benefits a deceased person.  However, they agree that supplicating in favor of the deceased people, invoking forgiveness for them, and giving charity on their behalf is beneficial to them. Most of the scholars hold that performing obligatory Hajj on behalf of the deceased do benefit them, They just differed on performing voluntary Hajj on their behalf. Evidence, however, implies that performing even voluntary Hajj on behalf of deceased people can benefit them.

This view is supported by  the narration on the authority of Ibn ‘Abbaas that the Prophet, sallallaahu ‘alayhi wa sallam, heard a pilgrim uttering Hajj rites on behalf of a man called Shubrumah, saying “Labayka on behalf of Shubrumah.” So the Prophet, sallallaahu ‘alayhi wa sallam, asked the man “Have you performed your own (obligatory)Hajj?  The man said, “No.” So, the Prophet, sallallaahu ‘alayhi wa sallam, told him “Perform your own Hajj first, then perform Hajj on behalf of Shubrumah.” Abu Daawood] [Ibn Maajah] [Al-Albaani: Saheeh]

The Prophet, sallallaahu ‘alayhi wa sallam, did not ask the man whether his Hajj on behalf of Shubrumah was obligatory or voluntary Hajj; that is he did not ask whether Shubramah ever performed Hajj or not, which indicates  generality. Also, the Prophet, sallallaahu ‘alayhi wa sallam, said to ‘Amr ibn Al-Aas : “If your father had acknowledged Tawheed, and then you fasted and gave charity on his behalf, this would benefit him.” [Ahmad] [Al-Albaani: Saheeh]

Thus, the Prophet, sallallaahu ‘alayhi wa sallam, conditioned that the deceased has to  be a Muslim so that he would benefit from the reward of good deeds that would be done on his behalf. Ibn Al-Qayyim studied this issue of granting the reward of doing good deeds to the dead persons in his book Ar-Rooh. He discussed the issue at length and did a great job. He chose the opinion adopted by Imaam Ahmad in this regard as well as many other scholars, who maintained that the deceased people benefit from the good deeds that are done on their behalf,  Hajj or other deeds.  This view was also chosen by a group of late Shaafi‘i scholars like An-Nawawi and others. It was also chosen by Al-Qurtubi from the Maaliki scholars; and supported by Ibn Abi Al-‘Izz,  the Hanafi scholar in his commentary on At-Tahaawiyyah; and maintained by Shaykh Al-Islam Ibn Taymiyyah .